This document provides examples and explanations of classless and variable-length subnet masking. It begins by defining classless addressing and variable-length blocks. It then provides 11 examples of finding network addresses, subnet masks, broadcast addresses, and designing subnets within allocated blocks. The examples demonstrate how to determine network prefixes and subnet masks and allocate addresses and subnets for different network needs.

1. Chapter 5
IP Addresses:
Classless Addressing
Objectives
Upon completion you will be able to:
• Understand the concept of classless addressing
• Be able to find the first and last address given an IP address
• Be able to find the network address given a classless IP address
• Be able to create subnets from a block of classless IP addresses
• Understand address allocation and address aggregation
TCP/IP Protocol Suite 1

2. 5.1 VARIABLE-LENGTH BLOCKS
In classless addressing variable-length blocks are assigned that belong
to no class. In this architecture, the entire address space (232 addresses)
is divided into blocks of different sizes.
The topics discussed in this section include:
Restrictions
Finding the Block
Granted Block
TCP/IP Protocol Suite 2

3. Figure 5.1 Variable-length blocks
TCP/IP Protocol Suite 3

4. ExamplE 1
Which of the following can be the beginning address
of a block that contains 16 addresses?
a. 205.16.37.32 b.190.16.42.44
c. 17.17.33.80 d.123.45.24.52
Solution
Only two are eligible (a and c). The address
205.16.37.32 is eligible because 32 is divisible by 16.
The address 17.17.33.80 is eligible because 80 is
divisible by 16.
TCP/IP Protocol Suite 4

5. ExamplE 2
Which of the following can be the beginning address
of a block that contains 256 addresses?
a.205.16.37.32 b.190.16.42.0
c.17.17.32.0 d.123.45.24.52
Solution
In this case, the right-most byte must be 0. As we
mentioned in Chapter 4, the IP addresses use base
256 arithmetic. When the right-most byte is 0, the
total address is divisible by 256. Only two addresses
are eligible (b and c).
TCP/IP Protocol Suite 5

6. ExamplE 3
Which of the following can be the beginning address
of a block that contains 1024 addresses?
a. 205.16.37.32 b.190.16.42.0
c. 17.17.32.0 d.123.45.24.52
Solution
In this case, we need to check two bytes because
1024 = 4 × 256. The right-most byte must be divisible
by 256. The second byte (from the right) must be
divisible by 4. Only one address is eligible (c).
TCP/IP Protocol Suite 6

7. Figure 5.2 Format of classless addressing address
TCP/IP Protocol Suite 7

8. Table 5.1 Prefix lengths
TCP/IP Protocol Suite 8

9. Note:
Classful addressing is a special case of
classless addressing.
TCP/IP Protocol Suite 9

10. ExamplE 4
What is the first address in the block if one of the
addresses is 167.199.170.82/27?
Solution
The prefix length is 27, which means that we must
keep the first 27 bits as is and change the remaining
bits (5) to 0s. The following shows the process:
Address in binary: 10100111 11000111 10101010 01010010
Keep the left 27 bits: 10100111 11000111 10101010 01000000
Result in CIDR notation: 167.199.170.64/27
TCP/IP Protocol Suite 10

11. ExamplE 5
What is the first address in the block if one of the
addresses is 140.120.84.24/20?
Solution
Figure 5.3 shows the solution. The first, second, and
fourth bytes are easy; for the third byte we keep the
bits corresponding to the number of 1s in that group.
The first address is 140.120.80.0/20.
See Next Slide
TCP/IP Protocol Suite 11

12. Figure 5.3 Example 5
TCP/IP Protocol Suite 12

13. ExamplE 6
Find the first address in the block if one of the
addresses is 140.120.84.24/20.
Solution
The first, second, and fourth bytes are as defined in
the previous example. To find the third byte, we write
84 as the sum of powers of 2 and select only the
leftmost 4 (m is 4) as shown in Figure 5.4. The first
address is 140.120.80.0/20.
See Next Slide
TCP/IP Protocol Suite 13

14. Figure 5.4 Example 6
TCP/IP Protocol Suite 14

15. ExamplE 7
Find the number of addresses in the block if one of
the addresses is 140.120.84.24/20.
Solution
The prefix length is 20. The number of addresses in
the block is 232−20 or 212 or 4096. Note that
this is a large block with 4096 addresses.
TCP/IP Protocol Suite 15

16. ExamplE 8
Using the first method, find the last address in the
block if one of the addresses is 140.120.84.24/20.
Solution
We found in the previous examples that the first
address is 140.120.80.0/20 and the number of
addresses is 4096. To find the last address, we need to
add 4095 (4096 − 1) to the first address.
See Next Slide
TCP/IP Protocol Suite 16

17. ExamplE 8 (Continued)
To keep the format in dotted-decimal notation, we
need to represent 4095 in base 256 (see Appendix B)
and do the calculation in base 256. We write 4095 as
15.255. We then add the first address to this number
(in base 255) to obtain the last address as shown
below:
140 . 120 . 80 . 0
15 . 255
-------------------------
140 . 120 . 95 . 255
The last address is 140.120.95.255/20.
TCP/IP Protocol Suite 17

18. ExamplE 9
Using the second method, find the last address in the
block if one of the addresses is 140.120.84.24/20.
Solution
The mask has twenty 1s and twelve 0s. The
complement of the mask has twenty 0s and twelve 1s.
In other words, the mask complement is
00000000 00000000 00001111 11111111
or 0.0.15.255. We add the mask complement to the
beginning address to find the last address.
See Next Slide
TCP/IP Protocol Suite 18

19. ExamplE 9 (Continued)
We add the mask complement to the beginning
address to find the last address.
140 . 120 . 80 . 0
0 . 0 . 15 . 255
----------------------------
140 . 120 . 95 . 255
The last address is 140.120.95.255/20.
TCP/IP Protocol Suite 19

20. ExamplE
10
Find the block if one of the addresses is
190.87.140.202/29.
Solution
We follow the procedure in the previous examples to
find the first address, the number of addresses, and
the last address. To find the first address, we notice
that the mask (/29) has five 1s in the last byte. So we
write the last byte as powers of 2 and retain only the
leftmost five as shown below:
See Next Slide
TCP/IP Protocol Suite 20

21. ExamplE 10 (Continued)
202 ➡ 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0
The leftmost 5 numbers are ➡ 128 + 64 + 0 + 0 + 8
The first address is 190.87.140.200/29
The number of addresses is 232−29 or 8. To find the last address,
we use the complement of the mask. The mask has twenty-nine
1s; the complement has three 1s. The complement is 0.0.0.7. If
we add this to the first address, we get 190.87.140.207/29. In
other words, the first address is 190.87.140.200/29, the last
address is 190.87.140.207/20. There are only 8 addresses in
this block.
TCP/IP Protocol Suite 21

22. ExamplE
11
Show a network configuration for the block in the previous
example.
Solution
The organization that is granted the block in the previous
example can assign the addresses in the block to the hosts in its
network. However, the first address needs to be used as the
network address and the last address is kept as a special
address (limited broadcast address). Figure 5.5 shows how the
block can be used by an organization. Note that the last
address ends with 207, which is different from the 255 seen in
classful addressing.
See Next Slide
TCP/IP Protocol Suite 22

23. Figure 5.5 Example 11
TCP/IP Protocol Suite 23

24. Note:
In classless addressing, the last
address in the block does not
necessarily end in 255.
TCP/IP Protocol Suite 24

25. Note:
In CIDR notation, the block granted is
defined by the first address and the
prefix length.
TCP/IP Protocol Suite 25

26. 5.2 SUBNETTING
When an organization is granted a block of addresses, it can create
subnets to meet its needs. The prefix length increases to define the
subnet prefix length.
The topics discussed in this section include:
Finding the Subnet Mask
Finding the Subnet Addresses
Variable-Length Subnets
TCP/IP Protocol Suite 26

27. Note:
In fixed-length subnetting, the number
of subnets is a power of 2.
TCP/IP Protocol Suite 27

28. ExamplE
12
An organization is granted the block 130.34.12.64/26.
The organization needs 4 subnets. What is the subnet
prefix length?
Solution
We need 4 subnets, which means we need to add two
more 1s (log2 4 = 2) to the site prefix. The subnet
prefix is then /28.
TCP/IP Protocol Suite 28

29. ExamplE
13
What are the subnet addresses and the range of
addresses for each subnet in the previous example?
Solution
Figure 5.6 shows one configuration.
See Next Slide
TCP/IP Protocol Suite 29

30. Figure 5.6 Example 13
TCP/IP Protocol Suite 30

31. ExamplE 13 (ContinuEd)
The site has 232−26 = 64 addresses. Each subnet has
232–28 = 16 addresses. Now let us find the first and last
address in each subnet.
1. The first address in the first subnet is 130.34.12.64/28,
using the procedure we showed in the previous examples.
Note that the first address of the first subnet is the first
address of the block. The last address of the subnet can
be found by adding 15 (16 −1) to the first address. The
last address is 130.34.12.79/28.
See Next Slide
TCP/IP Protocol Suite 31

32. ExamplE 13 (ContinuEd)
2.The first address in the second subnet is
130.34.12.80/28; it is found by adding 1 to the last
address of the previous subnet. Again adding 15 to
the first address, we obtain the last address,
130.34.12.95/28.
3. Similarly, we find the first address of the third
subnet to be 130.34.12.96/28 and the last to be
130.34.12.111/28.
4. Similarly, we find the first address of the fourth
subnet to be 130.34.12.112/28 and the last to be
130.34.12.127/28.
TCP/IP Protocol Suite 32

33. ExamplE
14
An organization is granted a block of addresses with the
beginning address 14.24.74.0/24. There are 232−24= 256
addresses in this block. The organization needs to have 11
subnets as shown below:
a. two subnets, each with 64 addresses.
b. two subnets, each with 32 addresses.
c. three subnets, each with 16 addresses.
d. four subnets, each with 4 addresses.
Design the subnets.
See Next Slide For One Solution
TCP/IP Protocol Suite 33

34. Figure 5.7 Example 14
TCP/IP Protocol Suite 34

35. ExamplE 14 (ContinutEd)
1. We use the first 128 addresses for the first two
subnets, each with 64 addresses. Note that the mask
for each network is /26. The subnet address for each
subnet is given in the figure.
2. We use the next 64 addresses for the next two
subnets, each with 32 addresses. Note that the mask
for each network is /27. The subnet address for each
subnet is given in the figure.
See Next Slide
TCP/IP Protocol Suite 35

36. ExamplE 14 (ContinutEd)
3. We use the next 48 addresses for the next three
subnets, each with 16 addresses. Note that the mask
for each network is /28. The subnet address for each
subnet is given in the figure.
4. We use the last 16 addresses for the last four
subnets, each with 4 addresses. Note that the mask for
each network is /30. The subnet address for each
subnet is given in the figure.
TCP/IP Protocol Suite 36

37. ExamplE
15
As another example, assume a company has three
offices: Central, East, and West. The Central office is
connected to the East and West offices via private,
point-to-point WAN lines. The company is granted a
block of 64 addresses with the beginning address
70.12.100.128/26. The management has decided to
allocate 32 addresses for the Central office and
divides the rest of addresses between the two offices.
Figure 5.8 shows the configuration designed by the
management.
See Next Slide
TCP/IP Protocol Suite 37

38. Figure 5.8 Example 15
TCP/IP Protocol Suite 38

39. ExamplE 15 (ContinuEd)
The company will have three subnets, one at Central, one at
East, and one at West. The following lists the subblocks
allocated for each network:
a. The Central office uses the network address
70.12.100.128/27. This is the first address, and the mask
/27 shows that there are 32 addresses in this network.
Note that three of these addresses are used for the
routers and the company has reserved the last address
in the sub-block. The addresses in this subnet are
70.12.100.128/27 to 70.12.100.159/27. Note that the
interface of the router that connects the Central subnet
to the WAN needs no address because it is a point-to-
point connection.
TCP/IP Protocol Suite See Next Slide 39

40. ExamplE 15 (ContinuEd)
b. The West office uses the network address
70.12.100.160/28. The mask /28 shows that there are
only 16 addresses in this network. Note that one of
these addresses is used for the router and the company
has reserved the last address in the sub-block. The
addresses in this subnet are 70.12.100.160/28 to
70.12.100.175/28. Note also that the interface of the
router that connects the West subnet to the WAN needs
no address because it is a point-to- point connection.
See Next Slide
TCP/IP Protocol Suite 40

41. ExamplE 15 (ContinuEd)
c. The East office uses the network address
70.12.100.176/28. The mask /28 shows that there are
only 16 addresses in this network. Note that one of
these addresses is used for the router and the company
has reserved the last address in the sub-block. The
addresses in. this subnet are 70.12.100.176/28 to
70.12.100.191/28. Note also that the interface of the
router that connects the East subnet to the WAN needs
no address because it is a point-to-point connection.
TCP/IP Protocol Suite 41

42. 5.3 ADDRESS ALLOCATION
Address allocation is the responsibility of a global authority called the
Internet Corporation for Assigned Names and Addresses (ICANN). It
usually assigns a large block of addresses to an ISP to be distributed to
its Internet users.
TCP/IP Protocol Suite 42

43. ExamplE
16
An ISP is granted a block of addresses starting with
190.100.0.0/16 (65,536 addresses). The ISP needs to
distribute these addresses to three groups of
customers as follows:
a. The first group has 64 customers; each needs 256
addresses.
b. The second group has 128 customers; each needs 128
addresses
c. The third group has 128 customers; each needs 64
addresses.
See Next Slide
TCP/IP Protocol Suite 43

44. ExamplE 16 (ContinuEd)
Design the subblocks and find out how many
addresses are still available after these allocations.
Solution
Figure 5.9 shows the situation.
See Next Slide
TCP/IP Protocol Suite 44

45. Figure 5.9 Example 16
TCP/IP Protocol Suite 45

46. ExamplE 16 (ContinuEd)
Group 1
For this group, each customer needs 256 addresses.
This means the suffix length is 8 (28 =256). The prefix
length is then 32 − 8 = 24. The addresses are:
1st Customer 190.100.0.0/24 190.100.0.255/24
2nd Customer 190.100.1.0/24 190.100.1.255/24
...
64th Customer 190.100.63.0/24 190.100.63.255/24
Total = 64 × 256 = 16,384
See Next Slide
TCP/IP Protocol Suite 46

47. ExamplE 16 (ContinuEd)
Group 2
For this group, each customer needs 128 addresses.
This means the suffix length is 7 (27 =128). The prefix
length is then 32 − 7 = 25. The addresses are:
1st Customer 190.100.64.0/25 190.100.64.127/25
2nd Customer 190.100.64.128/25 190.100.64.255/25
···
128th Customer 190.100.127.128/25 190.100.127.255/25
Total = 128 × 128 = 16,384
See Next Slide
TCP/IP Protocol Suite 47

48. ExamplE 16 (ContinuEd)
Group 3
For this group, each customer needs 64 addresses.
This means the suffix length is 6 (26 = 64). The prefix
length is then 32 − 6 = 26. The addresses are:
1st Customer 190.100.128.0/26 190.100.128.63/26
2nd Customer 190.100.128.64/26 190.100.128.127/26
···
128th Customer 190.100.159.192/26 190.100.159.255/26
Total = 128 × 64 = 8,192
See Next Slide
TCP/IP Protocol Suite 48

49. ExamplE 16 (ContinuEd)
Number of granted addresses to the ISP: 65,536
Number of allocated addresses by the ISP: 40,960
Number of available addresses: 24,576
TCP/IP Protocol Suite 49